The extension for mean curvature flow with finite integral curvature in Riemannian manifolds

被引：7

作者：

Xu HongWei ^{[1
]}

Ye Fei ^{[1
]}

Zhao EnTao ^{[1
]}

机构：

[1] Zhejiang Univ, Ctr Math Sci, Hangzhou 310027, Zhejiang, Peoples R China

来源：

SCIENCE CHINA-MATHEMATICS | 2011年 / 54卷 / 10期

基金：

中国国家自然科学基金; 中国博士后科学基金;

关键词：

mean curvature flow; Riemannian manifold; maximal existence; integral curvature; SUBMANIFOLDS;

D O I：

10.1007/s11425-011-4244-3

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We investigate the integral conditions to extend the mean curvature flow in a Riemannian manifold. We prove that the mean curvature flow solution with finite total mean curvature at a finite time interval [0, T) can be extended over time T. Moreover, we show that the condition is optimal in some sense.

引用

页码：2195 / 2204

页数：10

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